About semilinear low dimension Bessel PDEs

We prove existence and uniqueness of solutions of a semilinear PDE driven by a Bessel type generator$L^\delta$ with low dimension $0 < \delta < 1$. $L^\delta$ is a local operator, whose drift is thederivative of $x \mapsto \log (\vert x\vert)$:in particular it is a Schwartz distribution, whichis not the derivative of a continuous function.The solutions are intended in a duality (''weak'') sensewith respect to state space$L^2(\mathbb{R}_+, d\mu),$ $\mu$ being an invariant measure for the Bessel semigroup.